Asymptotic expension of large argument (see [1]}) :
\(\forall n\in \mathbb {N}^{*},\quad I_{n}(x)\underset{x\rightarrow +\infty }{\sim }\frac{e^{x}}{\sqrt{2\pi x}}\quad \mbox{ and }\quad K_{n}(x)\underset{x\rightarrow +\infty }{\sim }\sqrt{\frac{\pi }{2x}}e^{-x}.\) 
